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For a two-dimensional flow, the velocity field is
u = x i + y j x² + y² x² + y²
where i and j are the basis vectors in the x – y Cartesian coordinate system. Identify the CORRECT statements from below.
1. The flow is incompressible
2. The flow is unsteady
3. y-component of acceleration,ay = - y (x² + y²)²
4. x-component of acceleration,ax = -(x + y) (x² + y²)²
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- 2 and 3
- 1 and 3
- 1 and 2
- 3 and 4
Correct Option: B
| axu | + v | δx | δy |
| = | = | (x² + y²)(x² + y²) | (x² + y²) |
| ∴ ax = | (x² + y²)² |
| ay = u | + v | δx | δy |
| = | = | (x² + y²)3 | (x² + y²)² |
The velocity components are not functions of time, so flow is steady according to continuity equation,
Since it satisfies the above continuity equation for 2D and incompressible flow.
∴ The flow is incompressible.
